Resources tagged with: Visualising

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Broad Topics > Thinking Mathematically > Visualising

Square Corners

Age 7 to 11 Challenge Level:

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Quadrilaterals

Age 7 to 11 Challenge Level:

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Nine-pin Triangles

Age 7 to 11 Challenge Level:

How many different triangles can you make on a circular pegboard that has nine pegs?

Open Boxes

Age 7 to 11 Challenge Level:

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Putting Two and Two Together

Age 7 to 11 Challenge Level:

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Waiting for Blast Off

Age 7 to 11 Challenge Level:

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Single Track

Age 7 to 11 Challenge Level:

What is the best way to shunt these carriages so that each train can continue its journey?

Shunting Puzzle

Age 7 to 11 Challenge Level:

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Jigsaw Pieces

Age 7 to 11 Challenge Level:

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Display Boards

Age 7 to 11 Challenge Level:

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Inside Seven Squares

Age 7 to 11 Challenge Level:

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Four Triangles Puzzle

Age 5 to 11 Challenge Level:

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Knight's Swap

Age 7 to 11 Challenge Level:

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Counters

Age 7 to 11 Challenge Level:

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

A Square in a Circle

Age 7 to 11 Challenge Level:

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

Seeing Squares for Two

Age 5 to 11 Challenge Level:

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

Seeing Squares

Age 5 to 11 Challenge Level:

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

World of Tan 20 - Fractions

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the chairs?

The Development of Spatial and Geometric Thinking: the Importance of Instruction.

Age 5 to 11

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

World of Tan 18 - Soup

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?

Keep Your Distance

Age 11 to 14 Challenge Level:

Can you mark 4 points on a flat surface so that there are only two different distances between them?

World of Tan 6 - Junk

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the silhouette of the junk?

LOGO Challenge - Triangles-squares-stars

Age 11 to 16 Challenge Level:

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

World of Tan 13 - A Storm in a Tea Cup

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the convex shapes?

Square Coordinates

Age 11 to 14 Challenge Level:

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Fence It

Age 11 to 14 Challenge Level:

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Ten Hidden Squares

Age 7 to 14 Challenge Level:

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

On the Edge

Age 11 to 14 Challenge Level:

If you move the tiles around, can you make squares with different coloured edges?

Square It

Age 11 to 16 Challenge Level:

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Regular Rings 1

Age 7 to 11 Challenge Level:

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Put Yourself in a Box

Age 7 to 11 Challenge Level:

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

Twice as Big?

Age 7 to 11 Challenge Level:

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Endless Noughts and Crosses

Age 7 to 11 Challenge Level:

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

Reef and Granny

Age 7 to 11 Challenge Level:

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Framed

Age 11 to 14 Challenge Level:

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

Tetra Square

Age 11 to 14 Challenge Level:

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

Clocked

Age 11 to 14 Challenge Level:

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

Counting Cards

Age 7 to 11 Challenge Level:

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

World of Tan 7 - Golden Goose

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the plaque design?

Coloured Edges

Age 11 to 14 Challenge Level:

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

Zooming in on the Squares

Age 7 to 14

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

Fractional Triangles

Age 7 to 11 Challenge Level:

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Map Folding

Age 7 to 11 Challenge Level:

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

World of Tan 28 - Concentrating on Coordinates

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the playing piece?

Making Maths: Rolypoly

Age 5 to 11 Challenge Level:

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Little Boxes

Age 7 to 11 Challenge Level:

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

World of Tan 8 - Sports Car

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the sports car?

World of Tan 4 - Monday Morning

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?

World of Tan

Age 5 to 11 Challenge Level:

Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.

World of Tan 9 - Animals

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the camel and giraffe?